Which came first ... the Shakespeare name or the Shakspere man? Do any Marlowe-Shakespeareans (still) believe that a genius like their hero would choose an uneducated person like William Shakspere to pretend to be the author of the dedicatory prefaces he penned to the Earl of Southampton to launch Venus and Adonis and Rape of Lucrece his two epyllia in 1593 and '94? Clearly there was no need for a fake person at that time, especially considering that the addressee of the Dedications, a fellow Cambridge M.A., Henry Wriothesley knew Marley and his situation. But even if he didn't, would Stratford Shakspere be the man to present those mini-epic masterpieces? No, he wouldn't.
There was no need for a theatrical front until later in the decade in 1598, when it became clear that Shakespeare-the-pseudonymous-poet would write plays for the Chamberlain's Men. This didn't fall in place immediately; theatrical companies were reorganized. But the first Shakespeare plays in print were pseudonymously printed. Romeo and Juliet, Richard III, Merchant of Venice, etc. No need for a front until 1598, with the publication of Francis Meres' famous list of Shakespeare plays, and the first printing of a "Shakespeare" play: Loves Labours Lost by "W. Shakespere." This is also the time William got a 1/10th share of ticket sales along with several other shareholders.
It seems likely that William was invited to join the acting company because of his ambition, but more importantly because of his surname. However, it is possible that he was already part of the company as far back as 1594. Either way, Shakspere had nothing to do with the dead poet choosing his homophonic pseudonym—Will Shake-Speare—the best possible name he could have chosen.
There's a longer essay on this topic by Cynthia Morgan in The Marlowe Studies.